(14ab+3a)(2b2+4a)

To multiply the two polynomials \((14ab + 3a)(2b^2 + 4a)\), we can use the distributive property (also known as the FOIL method for binomials): \[ (14ab + 3a)(2b^2 + 4a) \] We'll distribute each term in the first polynomial to each term in the second polynomial: 1. \(14ab \cdot 2b^2 = 28ab^3\) 2. \(14ab \cdot 4a = 56a^2b\) 3. \(3a \cdot 2b^2 = 6ab^2\) 4. \(3a \cdot 4a = 12a^2\) Now, we combine all these results: \[ 28ab^3 + 56a^2b + 6ab^2 + 12a^2 \] Next, let's rearrange the terms in a standard form (typically arranging by the degree of each term): \[ 28ab^3 + 6ab^2 + 56a^2b + 12a^2 \] This is the final result of the multiplication. You can further simplify it if needed, but in this case, the expression is in its simplest polynomial form: \[ 28ab^3 + 6ab^2 + 56a^2b + 12a^2 \]